intro modeling simulation

7/27/2019 Intro Modeling Simulation

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Prof M S Prasad,

@2008

Based on open literature and reports . For special system model see Session II

presentations.


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Introduction to Simulation

A Simulation is the imitation of the operation of areal-world process or system over time

ASystem is defined to be a set of elements whichinteract or interrelated in some fashion Elements having no relationship with the set of

elements that have been chosen as system can not affect

the system hence irrelevant A System may consist of sub systems or may be a part of

a larger system

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Elements that often make up thesystem are calledEntitiesEntities that comprise a system need

not be tangible e.g, a queuing systemis made up of customers, queue andservers

Customers and servers are physical

entities but queue itself is a concept


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More components of a systemAnAttribute is a property of a system

AnActivity represents a time period of specifiedlength

State of system is defined to be that collection ofvariables necessary to describe the system at any time ,relative to the objective of the study In the study of a bank possible state variables are number of

busy tellers, number of customers waiting in the queue orbeing served, arrival and service times of the next customer

An Event is defined as an instantaneous occurrencethat may change the state of the system

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More terms of a system Endogenous used to describe the activities and

events occurring within a system

Exogenous is used to describe activities and events inthe environment that affect the system

In the bank arrival of a customer is exogenous eventand completion of service of a customer is endogenousevent

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Examples: Production System Entities Machines

Attributes (property of an entity) Speed , Capacity,

Breakdown rateActivities (time period of specified length) Welding,

Cutting, Stamping

Events breakdown

State variables Status of machines busy, idle ordown

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Examples: Communications System Entities Messages

Attributes (property of an entity) Length ,

DestinationActivities (time period of specified length)

Transmitting

Events arrival at destination

State variables Number of messages waiting to betransmitted

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Examples: Inventory System Entities Warehouse

Attributes (property of an entity) Capacity

Activities (time period of specified length) Issue,Receipt

Events Demand

State variables Level of inventory, Backlogged

demands

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Introduction to modelA model is a system that is used as a surrogate for

another system

Reason for using a model Helps in understanding the behaviour of a real system

before it is built

Cost of building and experimenting with a model is less

Models can be used to mitigate risk pilots can be

taught how to cope with wind sheer while landing Models have the capability of scale time or space in

favourable manner wind sheer can be produced ondemand

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Types of ModelsBroadly there are two types

Physical

(Scale models, prototype plants,)

Mathematical

(Analytical queuing models, linearprograms, simulation)

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Ten Types of Models Iconic - physical models that are images of the

real world; dimensions are usually scaled up ordown; for example, models of cars might be

constructed and tested in a wind tunnelAnalog - model that substitutes one set of

properties for another; may be iconic ormathematical; electric resistance often used as ananalog of the friction of a fluid flowing in a pipe;

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Ten Types of Models Stochastic - probabilistic model that usesrandomness to account for non measurablefactors (e.g., weather)

Deterministic - model that does not userandomness but uses explicit expressions forrelationships

Discrete - model where state variables change insteps as opposed to continuously with time (e.g.,number of cattle in a barn); may be deterministicor stochastic

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Ten Types of Models Continuous - model whose state variables change

continuously with time (e.g., biomass in a field);usually sets of differential equations used; initial

conditions required (can be difficult to obtain for somesystems!)

Combined - model where some state variables changecontinuously and others change in steps at event

times; for example, a field of hay might be modeledusing a combined approach with the biomass modeledcontinuously during growth and then as a discreteevent when harvested

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Types of Models Mathematical - abstract model usually written in

equation form

Object-oriented - use objects that are abstractions of

real world objects and develop relationships andactions between objects; comes from field of artificialintelligence

Heuristic - heuristics (rules) are used to model the

system; comes from field of artificial intelligence.

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Static Model

Dynamic Model

Lumped & distributed Models :distributed model use Partial diff equation to Explain spacevarying parameters.

In Lumped model the space variations are defined

in finite numbers making it a differential eqn,


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What is Simulation?A Simulation of a system is the operation of a

model, which is a representation of that system.

The model is amenable to manipulation whichwould be impossible, too expensive, or tooimpractical to perform on the system which itportrays.

The operation of the model can be studied, and,from this, properties concerning the behavior ofthe actual system can be inferred.

Introduction 16


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Applications:Designing and analyzing manufacturing systemsEvaluating H/W and S/W requirements for a

computer systemEvaluating a new military weapons system or tacticsDetermining ordering policies for an inventory

systemDesigning communications systems and message

protocols for them

Introduction 17


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Applications:(continued)Designing and operating transportation facilities such

as freeways, airports, subways, or ports

Evaluating designs for service organizations such ashospitals, post offices, or fast-food restaurants

Analyzing financial or economic systems

Introduction 18


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Types of Simulation Models

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System model

deterministic stochastic

static dynamic static dynamic

continuous discrete continuous discrete

Monte Carlo

simulation

Discrete-event

simulation

Continuous

simulation

Discrete-event

simulation

Continuous

simulation


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Stochastic vs. Deterministic

Stochastic simulation: a simulation that containsrandom (probabilistic) elements, e.g., Examples

Inter-arrival time or service time of customers at a restaurant orstore

Amount of time required to service a customer Output is a random quantity (multiple runs required to

analyze output)

Deterministic simulation: a simulation containing

no random elements Examples

Simulation of a digital circuit

Simulation of a chemical reaction based on differential equations

Output is deterministic for a given set of inputs05.06.2008 20


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Static vs. Dynamic Models Static models

Model where time is not a significant variable

Examples Determine the probability of a winning solitaire hand

Static + stochastic = Monte Carlo simulation Statistical sampling to develop approximate solutions to

numerical problems

Dynamic models Model focusing on the evolution of the system under

investigation over time

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Continuous vs. Discrete Discrete

State of the system is viewed as changing at discretepoints in time: arrival of a customer in a queuing system

An event is associated with each state transition Events contain time stamp

Continuous State of the system is viewed as changing continuously

across time: rise if water level in a dam System typically described by a set of differential

equations

Few systems in practice are wholly discrete orcontinuous

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Discrete & Continuous Systems Essential to remember that

A discrete simulation model is not always used to modela discrete system

Similarly, a continuous simulation model is not alwaysused for a continuous system

Simulation models may also be mixed both discreteand continuous

Choice of discrete or continuous simulationmodels is a function of Characteristics of the system

Objective of the study

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Discrete & Continuous Systems Communication channel

Modeled as discrete if characteristics of movement ofeach message is important

Modeled as continuous if f low of messages asaggregate over the channel is important

In this course we will study only

Models that are discrete, dynamic and stochastic

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Discrete event systems (DES) DES are dynamic systems which evolve in time by theoccurrence of events at possibly irregular timeintervals

DES abound in real-world applications Examples include traffic systems

flexible manufacturing systems

computer-communications systems

production lines flow networks.

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Discrete event systems (DES) Most of these systems can be modeled in terms of

discrete events whose occurrence causes the system tochange from one state to another

In designing, analyzing and operating such complexsystems, one is interested not only in performanceevaluation but also in sensitivity analysis andoptimization.

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Discrete event system simulation (DESS)

It is modeling of systems in which the state variablechanges only at a discrete set of points in time

Simulation models are analyzed by numerical

methods rather than by analytical methodsAnalytical methods apply deductive reasoning to solve

Differential calculus can be used to calculate EOQ

In case of simulation model is run rather thansolved

An artificial history of the system is generated (withthe help of computer) based on system characteristicsand observations are collected to be analyzed

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Steps in Simulation Study

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Problem Formulation

Setting objectives & Plan

Data Collection

Model Conceptualization

Verify model

Validate model

Fundamentallyan iterative

processModel Translation

Experimental Design


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Steps in Simulation Study

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Production run & Analysis

More runs?

Documentation & Reporting

Implementation

From previous slide


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Problem Formulation Initial step

Identify controllable and uncontrollable inputs

Identify constraints on the decision variables Define measure of system performance and an

objective function

Develop a preliminary model structure to

interrelate the inputs and the measure ofperformance

May be the problem needs reformulation as thestudy progresses

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Setting Objectives & PlanWhat do you (or the customer) hope to accomplish

with the model May be an end in itself

Predict the weather Train personnel to develop certain skills (e.g., driving)

More often a means to an end Optimize a manufacturing process or develop the most costeffective means to reduce traffic congestion in some part of a city

Often requires developing a business case to justifythe cost Improved efficiency will save the company $$$

Example: electronics Even so, may be hard to justify in lean times

Goals may not be known when you start theproject! One often learns things along the way

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Develop Conceptual Model An abstract (i.e., not directly executable) representationof the system

What should be included in model? What can be leftout?

What abstractions should be used Level of detail Often a variation on standard abstractions Example: transportation

Fluid flow? Queuing network? Cellular automation?

What metrics will be produced by the model? Appropriate choice depends on the purpose of the model

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Data Collection Regardless of the method used to collect the data, the

decision of how much to collect is a trade-off betweencost and accuracy

Constant inter play between construction of the modeland the collection of needed input

Changes with the degree of complexity of the model

Data should be collected for the validation as well

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Model translation Model requires great deal of information and

computation

Needs to be translated into computer recognizableformat using either special purpose or general purposelanguages

Focus of this course will be using Excel for model

buildingArena characteristics will be introduced

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Verification & Validation

Verification focuses on the internal consistency of amodel

Validation is concerned with the correspondencebetween the model and the reality

Validation is applied to those processes which seek todetermine whether or not a simulation is correct withrespect to the "real" system

Validation is concerned with the question "Are we

building the right system?

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Verification & ValidationVerification seeks to answer the question "Are we

building the system right?"

Verification checks that the implementation of the

simulation model (program) corresponds to the modelValidation checks that the model corresponds to

reality

Calibration checks that the data generated by the

simulation matches real (observed) data.

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Experimental DesignAlternatives to be simulated must be determined

Good experimental design Randomization

Replication Local control

For each system decisions needed Length of the initialization period

Length of the simulation run

Number of replication

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Production runs and analysis To measure performance of the simulation system so

designed

Also to determine if more runs needed till results areconsistent

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Documentation & Reporting Two types

Program

Needed if it is to be used again

May need to be applied for different system by differentpeople

For modification

Progress

Provides important written history of simulation project Should be frequent as the project progresses

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Implementation Success depends how well previous steps were

followed .

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M S Prasad : An avid researcher in the field ofSignal processing & Image processing, applicableto defence system. He has been designer of on Board computer

Navigation system, Multiple Target tracking for missiles he started thedigital GIS system in the country and has been responsible for having

a total digital military Ops room . In his span of career , he has beenNetwork security auditor for UNO classified organisations.He is the inventor most secure strategic system for India alongwithPositive Activation& Safing System.(PASS)

He holds 4 patents and has been awarded twice the Best scientist by defenceResearch organisation. Lately he is the chief evangelist of Cloud Security in ASIA.He is recipient of numerous national & International awards. He has published 28 papersin referred journals and 3 in Monographs


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intro modeling simulation

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